Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions

Satoshi Masaki, Junichi Segata

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the long time behavior of the solution to the quadratic nonlinear Klein–Gordon equation (NLKG) in two space dimensions: (Formula Presented), where □ = ∂t 2 − Δ is d’Alembertian. For a given asymptotic profile uap, we construct a solution u to (NLKG) which converges to uap as t → ∞. Here the asymptotic profile uap is given by the leading term of the solution to the linear Klein–Gordon equation with a logarithmic phase correction. Construction of a suitable approximate solution is based on Fourier series expansion of the nonlinearity.

Original languageEnglish
Pages (from-to)8155-8170
Number of pages16
JournalTransactions of the American Mathematical Society
Volume370
Issue number11
DOIs
Publication statusPublished - Jan 1 2018

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Asymptotic Profile
Nonlinear Klein-Gordon Equation
Nonlinear equations
Two Dimensions
Scattering
Fourier Expansion
Klein-Gordon Equation
Fourier series
Long-time Behavior
Linear equations
Series Expansion
Linear equation
Logarithmic
Approximate Solution
Nonlinearity
Converge
Term

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions. / Masaki, Satoshi; Segata, Junichi.

In: Transactions of the American Mathematical Society, Vol. 370, No. 11, 01.01.2018, p. 8155-8170.

Research output: Contribution to journalArticle

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